Permutation & Combination Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts
Permutations & Combination PRACTICE TEST [1 - EXERCISES]
Permutation & Combination Model Questions Set 1
Question : 16
There are 100 students in a college class of which 36 are boys studying statistics and 13 girls not studying statistics. If there are 55 girls in all, then the probability that a boy picked up at random is not studying statistics, is
a) 1/5
b) 2/5
c) 4/5
d) 3/5
e) None of these
Answer »Answer: (a)
There are 55 girls and 45 boys in the college.
Out of 45 boys, 36 are studying Statistics and 9 are not studying statistics.
∴ The probability that a boy picked up at random is not
studying Statistics = $9/{45}$ = $1/5$
Question : 17
In how many ways can six different rings be worn on four fingers of one hand ?
a) 15
b) 12
c) 16
d) 10
e) None of these
Answer »Answer: (a)
Required number of ways
= ways of selecting 4 objects out of 6 given objects
= $^6C_4$ = ${6 × 5}/2$ = 15
Question : 18
From amongst 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done ?
a) 1240
b) 1250
c) 1800
d) 1260
e) None of these
Answer »Answer: (d)
Principal can be appointed in 36 ways.
Vice principal can be appointed in the remaining 35 ways.
Total number of ways = 36 × 35 = 1260
Question : 19
The committee should consist of 2 Professors, 2 Teachers and 1 Reader?
a) 55
b) 225
c) 90
d) 450
e) None of these
Answer »Answer: (d)
Total number of ways to form committee
= $^5C_2 × ^6C_2 × ^3C_1$ = ${5 × 4}/{1 × 2}$ × ${6 × 5}/{1 × 2}$ × $3/1$= 10 × 15 × 3 = 450
Question : 20
In how many different ways can the letters of the word 'OFFICES' be arranged?
a) 1850
b) 5040
c) 1680
d) 2520
e) None of these
Answer »Answer: (d)
In word 'offices', there are 7 letters and F comes two times.
Required number of ways = ${7!}/{2!}$ = ${7 × 6 × 5 × 4 × 3 × 2!}/{2!}$ = 2520
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